My program for finding dual binary-ternary palindromes rolled over to 105 bits yesterday as expected, then immediately jumped to 67 trits. I terminated it. So the current ceiling is 3^66, which is about 2^104.6, 10^31.5, or e^72.5. It's about 800 million times higher than Giovanni Resta's ceiling of 2^75, and 4 times higher than the dual palindrome I discovered last week. In other words, a 10th dual binary-ternary palindrome, if it exists -- and I'm sure it does -- would be larger than 3^66. A correction to my previous message: Where I said "about 1.8 (3^10/2^9)" the 9 should be 15. In the same message I said that I suspected that the statistics on dual binary *balanced* ternary palindromes would be the same as on dual binary ternary palindromes. I gain a factor of two in one place (the middle digit can be plus or minus 1), but lose it in another (the leading digit must be +1; for standard ternary it can be 1 or 2). The actual palindromes would be different (though I had noticed that 1 and 6643 are palindromes in balanced ternary as well as in binary and standard ternary), but I figured that the long range probabilities ought to be exactly the same. But I've taken my first look at binary balanced ternary palindromes, and it looks like they're much more common. Does anyone have any idea how this can be? What am I overlooking? The first few are 1, 7, 73, 511, 5461, 6211, 6643, 306601, 432331, 471655, 6815731, 7036267, 21583141. (Not in OEIS.) I was feeling lazy, so to "calculate" these I wrote a one-line "program": cut -f 2 -d\ b006995.txt b134027.txt | sort -n | uniq -c | grep \ 2\ | cut -c 6-99 | sort -n (This made use of two files downloaded from OEIS, of course.)